Orders of Magnitude of Probabilities.

Introduction

We, humans, live in the world of common events. The majority of events we observe on a day-to-day basis are familiar, meaning they are common enough not to be bothered to notice. We rarely see unfamiliar events; they are usually rare (for us). This is why humans are bad at distinguishing different orders of rarity. Not all “unlikely” things are the same.
More often than not, I hear people say “it’s a rare event” or “this is unlikely”. We’d casually drop something like one in a million chance… We use it interchangeably and usually don’t give it much thought on how different these scales are.
This is the qualitative step between the two. Each additional zero represents a very different regime. Science calls it orders of magnitude.

In this post, I want to show how different rare events are. In fact, they’re very different.
We’ll climb through the orders of magnitude from something that is quite common, like 1 in 10, to rare events, like 1 in 1,000 and 1 in 100,000, and demonstrate that they are, in fact, quite different.

NOTE: Some examples that will be presented below are not exact probabilities; they’re accurate to the order of magnitude and for the peg reference only. For more precise poker probabilities, use reference table .

Common Everyday Frequencies

1 in 2

• The starting point
• 50% probability
• Coin Flip

1 in 3

• 33% probability

1 in 5

• 20 % probability
• Roughly high card in poker

1 in 10

• 10% probability
• A person in the meeting or friend group
• Event happening every couple of weeks

1 in 20

• 5% probability
• Three-of-a-kind, straight in poker

1 in 50

• 2% probability
• Full house in poker
• Event happening every couple of month

Stack of a 52-card deck.

Ocassional Periodic Frequencies

1 in 100

• 1% probability
• Large lecture hall or company
• Event happens few times a year

1 in 500

• 0.2% probability
• Event happens once a year
• Four-of-a-kind hand in poker

1 in 1,000

• 0.1% probability
• Your small town neighborhood
• Happens once in few years

A pile of cards

Rair and Unlikely Frequencies

1 in 10,000

• 0.01% probability
• Someone in a town
• Once every few decades

1 in 100,000

• 0.001% probability
• Someone in the small city
• Once in a lifetime

1 in 1,000,000

• 0.0001%
• Someone in the big city
• Once in the several lifetimes

A building of a cards

Almost Impossible Frequencies

1 in 10,000,000

• 0.000001%
• Someone in the metro area
• About the odds of winning a national lottery jackpot

1 in 100,000,000

• 0.0000001%
• Someone in the nation/country
• Once in ..

A mountain of a cards

Conclusion

This post intended to be a visualization of the real difference between orders of magnitudes.